In a large pot over medium heat, melt the butter. Add the garlic, onion, carrots, and celery, and cook until the vegetables are softened, about 5 minutes.
Add the potatoes, chicken broth, thyme, black pepper, and cayenne pepper, if using. Bring to a boil, then reduce heat and simmer for 20 minutes, or until the potatoes are tender.
Add the half-and-half cream and cheddar cheese, and stir until the cheese is melted. Season with salt and pepper, to taste.
Serve hot with a sprinkle of cheese, sour cream, or chives, if desired.
Interesting Facts
This soup can be made with any variety of potatoes, including Yukon Gold, Red, and Sweet potatoes.
The soup can be served chunky or blended until smooth.
This soup can be made ahead of time and reheated for later.
Leftovers can be stored in the refrigerator for up to 3 days or frozen for up to 1 month.